1. Field of the Invention
This invention is related in general to the field of white-light interferometry. In particular, the invention relates to the removal of bat wings from discontinuous surface profiles using a combination of coherence and phase data.
2. Description of the Related Art
One method of determining surface height involves the use of a broad-spectral-width light source in an interferometer and measuring the degree of modulation contrast as a function of optical path difference (OPD). The approach is typically referred to in the art as vertical scanning interferometry (VSI). Due to the large spectral bandwidth of the source, the coherence length of the source is short and good contrast fringes are obtained only when the two paths of the interferometer are closely matched in length. By looking at the position of the sample surface for which the fringe contrast is maximum while the optical path difference is varied, the height variations across the sample can be determined. In this measurement there are no height ambiguities or focus errors because the interferometer is adjusted to have the sample in focus when the OPD is zero.
There are many algorithms for finding the coherence peak of VSI correlograms. However, while this is a very good technique for measuring many surfaces, it does not work well in the vicinity of step heights that are less than the coherence length of the light source. A diffraction effect at the discontinuity causes the coherence envelope of the correlogram to skew and the peak to shift. The problem has been referred to in the art as a xe2x80x9cbat wingxe2x80x9d effect because of the shape of the erroneous information produced by VSI data. Bat wings are produced by every well-established coherence-peak-sensing algorithm used in the art and it can be shown that diffraction effects modify the coherence envelope more than the phase of the correlogram. Thus, phase-shifting interferometry (PSI), herein also referred to as phase sensing, is preferred when steplike discontinuities cause bat wings.
FIG. 1 illustrates bat-wing effects obtained using various VSI algorithms in measuring the surface profile of a 460-nm height standard (VLSI Standards Inc., SHS 4600 xc3x85). FIG. 1A is a surface profile processed using a centroid algorithm, as disclosed by Ai et al. in U.S. Pat. No. 5,633,715. FIG. 1B is a profile obtained from the centroid of the recovered modulation contrast by the Fourier transform algorithm. FIG. 1C is a profile obtained from the centroid of the recovered modulation contrast by the Hilbert transform algorithm. FIG. 1D is a profile obtained from the phase slope in the Fourier domain. The light source used in the measurement had a coherence length of 1.2 microns. Bat wings clearly appear in all profiles because the coherence length of the light source exceeds the step height. The top portion close to the edge of the step discontinuity, whose height is less than the coherence length, typically appears higher and the bottom portion appears lower than they actually are. From FIG. 1 it is clear that the effect is named bat wings because of its appearance.
The combination of phase and coherence-peak sensing techniques (PSI with VSI) has been explored for some time to provide the advantages of both methods. U.S. Patent No. 5,133,601 to Cohen et al. discloses a technique, referred to as PSI xe2x80x9con the fly,xe2x80x9d whereby the resolution of VSI is improved by calculating phase around the peak of the coherence envelope. U.S. Patent No. 5,471,303 to Ai et al. combines independent VSI and PSI data to improve the accuracy of height measurements in steep regions and in areas with large inter-pixel steps in the test surface. In U.S. Patent No. 5,953,124, Deck further refines the combination of VSI and PSI analysis applied to a single 3-D interferogram to produce an improved height profile. However, no experimental results have been reported that teach the removal of bat wings. This invention is directed at providing a method and apparatus for eliminating bat-wing effects using a coherence-peak-sensing technique in combination with a phase-unwrapping algorithm.
The primary objective of this invention is a method for removing bat-wing effects from the surface profile of step discontinuities that are less than the coherence length of the light used in vertical scanning interferometry.
Another object is a procedure that produces an improved surface profile by combining coherence-peak detection with phase measurement using vertical scanning interferometry data and phase unwrapping to eliminate 2xcfx80 ambiguities.
Finally, a goal of the invention is a procedure that is suitable for implementation with relatively minor modifications to existing interference microscope objectives and interferometric surface profilers.
According to these and other objectives, the present invention consists of performing white-light vertical scanning interferometry to produce a three-dimensional interferogram corresponding to a sample surface. A first height profile is obtained from the correlogram using a coherence-peak-sensing technique. A second height profile is obtained from phase measurements. The two profiles are compared, and phase ambiguities are removed according to the invention using a phase-unwrapping algorithm that eliminates the effects of diffraction at the edges of relatively smooth surfaces that are separated by step discontinuities within the coherence length of the light source of the system. According to one aspect of the invention, the unwrapping step is carried out starting from pixels in relatively smooth areas of the sample surface and moving toward pixels at the edge of step discontinuities. Thus, the unwrapping process is designed to progress from areas of reliable data, such as evidenced by a high energy profile, toward step boundaries, where the energy profile is lowest.
According to another aspect of the invention, the unwrapping algorithm includes a novel step whereby the differences in height between two adjacent pixels obtained both by coherence-peak and by phase measurements are compared to a predetermined height considered empirically to be approximately as large as the largest interpixel diffraction effect produced by the coherence-peak technique. Since it has been established that diffraction effects cause greater artifacts in the coherence envelope than in the phase data, in each instance where the inter-pixel height difference calculated by coherence-peak detection is smaller and the inter-pixel height difference calculated by phase is larger than the selected height, the phase measurement is corrected by 2xcfx80 increments (i.e., height increments of fxcex/4, as defined below) so that both coherence and phase inter-pixel height differences are within the selected height. In practice, it was determined that approximately xc2xc the mean wavelength of the light source is a suitable value for the selected height when measuring smooth flat and round surfaces.
This additional step in the unwrapping procedure has been found to practically remove all bat-wing effects from profiles obtained by phase measurement. The resulting quality of the height data in each of the step regions is thus kept to within the resolution of the PSI measurements even at the step edges.
Various other purposes and advantages of the invention will become clear from its description in the specification that follows and from the novel features particularly pointed out in the appended claims. Therefore, to the accomplishment of the objectives described above, this invention consists of the features hereinafter illustrated in the drawings, fully described in the detailed description of the preferred embodiment and particularly pointed out in the claims. However, such drawings and description disclose but one of the various ways in which the invention may be practiced.